document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935882>Question 935882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that a cubic function f(x)=ax^3+bx^2+cx+d can be factored into two terms,one of which is (x-r). Find the other term using  (synthetic division) and answer the questions below.<BR>\n" );
document.write( "(1) ax^3+bx^2+cx+d = (x-r) ( ..........)<BR>\n" );
document.write( "(2) what must be true about ar^3 + br^2 +cr +d ? ...<BR>\n" );
document.write( "(3 what does this tell us about the value of f(r)? ... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569252 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> answer to question 1:\r<BR>\n" );
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document.write( "ax^3 + bx^2 + cx + d = (x-r) * (  ax^2 + (ra+b)x + (r^2a+rb+c)  )\r<BR>\n" );
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document.write( "answer to question 2:\r<BR>\n" );
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document.write( "ar^3 + br^2 + cr + d must be equal to 0\r<BR>\n" );
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document.write( "this is because r is a root of the equation which means that the value of f(r) must be equal to 0.\r<BR>\n" );
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document.write( "answer to question 3:\r<BR>\n" );
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document.write( "value of f(r) must be equal to 0.\r<BR>\n" );
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document.write( "this is because f(r) is equal to ar^3 + br^2 + cr + d\r<BR>\n" );
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document.write( "when r is a root, f(r) will be equal to 0.\r<BR>\n" );
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document.write( "r is a root when the remainder of the division by (x-r) is equal to 0.\r<BR>\n" );
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document.write( "when r is not a root, f(r) will be equal to the remainder of the division.\r<BR>\n" );
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document.write( "the synthetic division is shown below:\r<BR>\n" );
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document.write( "the first part shows the steps in the synthetic division.<BR>\n" );
document.write( "the second part shows the resulting equation after the division has been performed.<BR>\n" );
document.write( "the third part shows that the remainder must be equal to 0 if r is a root of the equation which occurs if (x-r) is a factor of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/010202.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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